2010008808
Level:
B
Factor the expression: \[4(3y - x)^2 - 25(y - 2x)^2\]
\((8x + y)(11y - 12x)\)
\((8x + y)(11y + 8x)\)
\((y - 12x)(11y - 12x)\)
\((y - 12x)(11y + 8x)\)
Polynomials and fractions
2010008809
Level:
B
Factor the expression: \[(4 + a)(a - 3) - (3 - a)^2 - 3(a - 3)(2a + 1)\]
\(2(a - 3)(2 - 3a)\)
\(2(a - 3)(3a - 2)\)
\(2(3 - a)(2a + 1)\)
\(2(a - 3)(2a + 1)\)
2010008810
Level:
B
Factor the expression: \[(2 - b)(b -7) - 5(b -7)(2b - 3) - (7 -b)^2\]
\(12(b - 7)(2 - b)\)
\(12(b - 7)(b - 2)\)
\(10(b - 7)(1 - b)\)
\(10(b - 7)(b - 1)\)
9000039301
Level:
B
Given formula for an acceleration of the motion in the form
\[
a = \frac{v - v_{0}}
{t} ,
\]
find the initial velocity \(v_{0}\).
\(v_{0} = v - at\)
\(v_{0} = vat\)
\(v_{0} = v + at\)
\(v_{0} = at - v\)
9000039302
Level:
B
Find \(N\),
the number of the turns, as a function of the other variables in the formula for the
magnetic induction of a solenoid.
\[
B =\mu \frac{NI}
{l}
\]
\(N = \frac{Bl}
{\mu I} \)
\(N = \frac{Bl\mu }
{I} \)
\(N = B -\mu \frac{I}
{l} \)
\(N = \frac{Bl}
{\mu } - I\)
9000039303
Level:
B
Find the time \(t\)
as a function of the other variables in the formula for the distance of a motion in the
form \(s = v_{0}t + s_{0}\).
\(t = \frac{s-s_{0}}
{v_{0}} \)
\(t = \frac{s}
{t+s_{0}} \)
\(t = \frac{s+s_{0}}
{v_{0}} \)
\(t = \frac{v_{0}}
{s-s_{0}} \)
9000039304
Level:
B
Find the focus length \(f\)
as a function of the other variables from the following equation relating this distance with object
and image distances \(a\)
and \(a'\).
\[
\frac{1}
{f} = \frac{1}
{a} + \frac{1}
{a'}
\]
\(f = \frac{aa'}
{a+a'}\)
\(f = \frac{a-a'}
{a+a'}\)
\(f = a + a'\)
\(f = \frac{a}
{a'}\)
9000039305
Level:
B
Find \(m_{1}\)
as a function of the other variables from the following mixing equation.
\[
w_{1}m_{1} + w_{2}m_{2} = w_{3}m_{3}
\]
\(m_{1} = \frac{w_{3}m_{3}-w_{2}m_{2}}
{w_{1}} \)
\(m_{1} = \frac{w_{3}m_{3}w_{2}m_{2}}
{w_{1}} \)
\(m_{1} = \frac{w_{3}m_{3}+w_{2}m_{2}}
{w_{1}} \)
\(m_{1} = \frac{w_{2}m_{2}-w_{3}m_{3}}
{w_{1}} \)
9000079202
Level:
B
Find the set \(M\)
of all the real \(x\)
for which the following expression is not a well defined number.
\[
\frac{x - 4}
{x^{3} - 16x}
\]
\(M = \{ - 4;0;4\}\)
\(M = \{ - 4;4\}\)
\(M = \{0;4\}\)
\(M = \{0\}\)
9000079204
Level:
B
Find the domain of the following expression.
\[
\frac{x^{2} - x}
{x + 1} : \frac{x^{2} - 1}
{x^{2} + 2x + 1}
\]
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\setminus \{ - 1;0;1\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1;0\}\)